Patients receive oral sorafenib tosylate twice daily on days 1-14. Patients then undergo transarterial chemoembolization (TACE) comprising doxorubicin hydrochloride and mitomycin C on days 17-19*. Patients then receive oral sorafenib tosylate twice daily beginning after recovery from TACE and continuing in the absence of disease progression or unacceptable toxicity.